Year: 2021
Author: Yiming Gao, Chunlin Wu
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 3 : pp. 395–430
Abstract
Multi-channel/modality image joint reconstruction has gained much research interest in recent years. In this paper, we propose to use a nonconvex and non-Lipschitz joint regularizer in a general variational model for joint reconstruction under additive measurement noise. This framework has good ability in edge-preserving by sharing common edge features of individual images. We study the lower bound theory for the non-Lipschitz joint reconstruction model in two important cases with Gaussian and impulsive measurement noise, respectively. In addition, we extend previous works to propose an inexact iterative support shrinking algorithm with proximal linearization for multi-channel image reconstruction (InISSAPL-MC) and prove that the iterative sequence converges globally to a critical point of the original objective function. In a special case of single channel image restoration, the convergence result improves those in the literature. For numerical implementation, we adopt primal dual method to the inner subproblem. Numerical experiments in color image restoration and two-modality undersampled magnetic resonance imaging (MRI) reconstruction show that the proposed non-Lipschitz joint reconstruction method achieves considerable improvements in terms of edge preservation for piecewise constant images compared to existing methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0029
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 3 : pp. 395–430
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Joint reconstruction multi-modality multi-channel variational method non-Lipschitz lower bound theory.
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